There are a few key differences between alligators and crocodiles that make them easily distinguishable.
First of all, Crocodiles and Alligators are part of 2 separate families, Crocodylidae and Alligatoridae respectively.
Crocodiles have a long, narrow, V-Shaped snout. Alligators have a wider. U-Shaped snout:

The alligator's wider snout allows for more crushing power; strong enough to crack turtle shells. The crocodile's narrow snout is less equipped for cracking turtle shells, but still very powerful, capable of bite strengths of 5,000 lbs/square inch.

Another difference between alligators and crocodiles is the presence or absence of viewable teeth. Crocodile's top and bottom teeth are viewable from the side, whereas alligator's bottom teeth are not.
In general, alligators are smaller and more docile, if you consider 14 feet small compared to the 19 feet of a crocodile, which are comparatively more aggressive.
Alligators which appear black are generally darker than crocodiles, which have an olive brown hide.